I never located the problem, but I fixed it.
After I put the new coils on and it wouldn't light due to the igniter not heating up, I decided to use jumper wires to bypass each separate part in the circuit. I removed each wire from its spade and then pushed it back on to ensure I wouldn't have any difficulties using the jumpers when the time came.
Just for the hell of it I tried to light it off one more time, and guess what? It worked flawlessly. Now, I know each wire was on the right connector, and I didn't jar any of them during all of this, so it had to be one of them that wasn't making the connection to complete the circuit.
So, before you go off the deep end, remove and replace your wires to ensure a good connection before you make any other decisions.